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A246194
Number of endofunctions on [n] where the smallest cycle length equals 7.
2
720, 40320, 1632960, 60480000, 2213719200, 82771476480, 3211179491520, 130241382036480, 5541589755702000, 247667354552217600, 11627089698327143040, 573008938660751523840, 29613698207957813302080, 1602975684200327700480000, 90757379602253683020931200
OFFSET
7,1
LINKS
FORMULA
a(n) ~ (exp(-49/20) - exp(-363/140)) * n^n. - Vaclav Kotesovec, Aug 21 2014
MAPLE
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
b(n-i*j, i+1), j=0..n/i)))
end:
A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
a:= n-> A(n, 7) -A(n, 8):
seq(a(n), n=7..25);
CROSSREFS
Column k=7 of A246049.
Sequence in context: A342074 A055361 A092716 * A246614 A291113 A246217
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 18 2014
STATUS
approved